/* bignumber.js v1.3.0 https://github.com/MikeMcl/bignumber.js/LICENCE */

/* jslint bitwise: true, eqeq: true, plusplus: true, sub: true, white: true, maxerr: 500 */

/* global module */

/*
  bignumber.js v1.3.0
  A JavaScript library for arbitrary-precision arithmetic.
  https://github.com/MikeMcl/bignumber.js
  Copyright (c) 2012 Michael Mclaughlin <M8ch88l@gmail.com>
  MIT Expat Licence
*/

/*********************************** DEFAULTS ************************************/

/*
 * The default values below must be integers within the stated ranges (inclusive).
 * Most of these values can be changed during run-time using BigNumber.config().
 */

/*
 * The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP,
 * MAX_EXP, and the argument to toFixed, toPrecision and toExponential, beyond
 * which an exception is thrown (if ERRORS is true).
 */
var MAX = 1E9,                                   // 0 to 1e+9

    // Limit of magnitude of exponent argument to toPower.
    MAX_POWER = 1E6,                             // 1 to 1e+6

    // The maximum number of decimal places for operations involving division.
    DECIMAL_PLACES = 20,                         // 0 to MAX

    /*
     * The rounding mode used when rounding to the above decimal places, and when
     * using toFixed, toPrecision and toExponential, and round (default value).
     * UP         0 Away from zero.
     * DOWN       1 Towards zero.
     * CEIL       2 Towards +Infinity.
     * FLOOR      3 Towards -Infinity.
     * HALF_UP    4 Towards nearest neighbour. If equidistant, up.
     * HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
     * HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
     * HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
     * HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
     */
    ROUNDING_MODE = 4,                           // 0 to 8

    // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]

    // The exponent value at and beneath which toString returns exponential notation.
    // Number type: -7
    TO_EXP_NEG = -7,                             // 0 to -MAX

    // The exponent value at and above which toString returns exponential notation.
    // Number type: 21
    TO_EXP_POS = 21,                             // 0 to MAX

    // RANGE : [MIN_EXP, MAX_EXP]

    // The minimum exponent value, beneath which underflow to zero occurs.
    // Number type: -324  (5e-324)
    MIN_EXP = -MAX,                              // -1 to -MAX

    // The maximum exponent value, above which overflow to Infinity occurs.
    // Number type:  308  (1.7976931348623157e+308)
    MAX_EXP = MAX,                               // 1 to MAX

    // Whether BigNumber Errors are ever thrown.
    // CHANGE parseInt to parseFloat if changing ERRORS to false.
    ERRORS = true,                               // true or false
    parse = parseInt,                            // parseInt or parseFloat

/***********************************************************************************/

    P = BigNumber.prototype,
    DIGITS = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_',
    outOfRange,
    id = 0,
    isValid = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
    trim = String.prototype.trim || function () {return this.replace(/^\s+|\s+$/g, '')},
    ONE = BigNumber(1);


// CONSTRUCTOR


/*
 * The exported function.
 * Create and return a new instance of a BigNumber object.
 *
 * n {number|string|BigNumber} A numeric value.
 * [b] {number} The base of n. Integer, 2 to 64 inclusive.
 */
function BigNumber( n, b ) {
    var e, i, isNum, digits, valid, orig,
        x = this;

    // Enable constructor usage without new.
    if ( !(x instanceof BigNumber) ) {
        return new BigNumber( n, b )
    }

    // Duplicate.
    if ( n instanceof BigNumber ) {
        id = 0;

        // e is undefined.
        if ( b !== e ) {
            n += ''
        } else {
            x['s'] = n['s'];
            x['e'] = n['e'];
            x['c'] = ( n = n['c'] ) ? n.slice() : n;
            return;
        }
    }

    // If number, check if minus zero.
    if ( typeof n != 'string' ) {
        n = ( isNum = typeof n == 'number' ||
            Object.prototype.toString.call(n) == '[object Number]' ) &&
                n === 0 && 1 / n < 0 ? '-0' : n + '';
    }

    orig = n;

    if ( b === e && isValid.test(n) ) {

        // Determine sign.
        x['s'] = n.charAt(0) == '-' ? ( n = n.slice(1), -1 ) : 1;

    // Either n is not a valid BigNumber or a base has been specified.
    } else {

        // Enable exponential notation to be used with base 10 argument.
        // Ensure return value is rounded to DECIMAL_PLACES as with other bases.
        if ( b == 10 ) {

            return setMode( n, DECIMAL_PLACES, ROUNDING_MODE );
        }

        n = trim.call(n).replace( /^\+(?!-)/, '' );

        x['s'] = n.charAt(0) == '-' ? ( n = n.replace( /^-(?!-)/, '' ), -1 ) : 1;

        if ( b != null ) {

            if ( ( b == (b | 0) || !ERRORS ) &&
              !( outOfRange = !( b >= 2 && b < 65 ) ) ) {

                digits = '[' + DIGITS.slice( 0, b = b | 0 ) + ']+';

                // Before non-decimal number validity test and base conversion
                // remove the `.` from e.g. '1.', and replace e.g. '.1' with '0.1'.
                n = n.replace( /\.$/, '' ).replace( /^\./, '0.' );

                // Any number in exponential form will fail due to the e+/-.
                if ( valid = new RegExp(
                  '^' + digits + '(?:\\.' + digits + ')?$', b < 37 ? 'i' : '' ).test(n) ) {

                    if ( isNum ) {

                        if ( n.replace( /^0\.0*|\./, '' ).length > 15 ) {

                            // 'new BigNumber() number type has more than 15 significant digits: {n}'
                            ifExceptionsThrow( orig, 0 );
                        }

                        // Prevent later check for length on converted number.
                        isNum = !isNum;
                    }
                    n = convert( n, 10, b, x['s'] );

                } else if ( n != 'Infinity' && n != 'NaN' ) {

                    // 'new BigNumber() not a base {b} number: {n}'
                    ifExceptionsThrow( orig, 1, b );
                    n = 'NaN';
                }
            } else {

                // 'new BigNumber() base not an integer: {b}'
                // 'new BigNumber() base out of range: {b}'
                ifExceptionsThrow( b, 2 );

                // Ignore base.
                valid = isValid.test(n);
            }
        } else {
            valid = isValid.test(n);
        }

        if ( !valid ) {

            // Infinity/NaN
            x['c'] = x['e'] = null;

            // NaN
            if ( n != 'Infinity' ) {

                // No exception on NaN.
                if ( n != 'NaN' ) {

                    // 'new BigNumber() not a number: {n}'
                    ifExceptionsThrow( orig, 3 );
                }
                x['s'] = null;
            }
            id = 0;

            return;
        }
    }

    // Decimal point?
    if ( ( e = n.indexOf('.') ) > -1 ) {
        n = n.replace( '.', '' );
    }

    // Exponential form?
    if ( ( i = n.search( /e/i ) ) > 0 ) {

        // Determine exponent.
        if ( e < 0 ) {
            e = i;
        }
        e += +n.slice( i + 1 );
        n = n.substring( 0, i );

    } else if ( e < 0 ) {

        // Integer.
        e = n.length;
    }

    // Determine leading zeros.
    for ( i = 0; n.charAt(i) == '0'; i++ ) {
    }

    b = n.length;

    // Disallow numbers with over 15 significant digits if number type.
    if ( isNum && b > 15 && n.slice(i).length > 15 ) {

        // 'new BigNumber() number type has more than 15 significant digits: {n}'
        ifExceptionsThrow( orig, 0 );
    }
    id = 0;

    // Overflow?
    if ( ( e -= i + 1 ) > MAX_EXP ) {

        // Infinity.
        x['c'] = x['e'] = null;

    // Zero or underflow?
    } else if ( i == b || e < MIN_EXP ) {

        // Zero.
        x['c'] = [ x['e'] = 0 ];
    } else {

        // Determine trailing zeros.
        for ( ; n.charAt(--b) == '0'; ) {
        }

        x['e'] = e;
        x['c'] = [];

        // Convert string to array of digits (without leading and trailing zeros).
        for ( e = 0; i <= b; x['c'][e++] = +n.charAt(i++) ) {
        }
    }
}


// CONSTRUCTOR PROPERTIES/METHODS


BigNumber['ROUND_UP'] = 0;
BigNumber['ROUND_DOWN'] = 1;
BigNumber['ROUND_CEIL'] = 2;
BigNumber['ROUND_FLOOR'] = 3;
BigNumber['ROUND_HALF_UP'] = 4;
BigNumber['ROUND_HALF_DOWN'] = 5;
BigNumber['ROUND_HALF_EVEN'] = 6;
BigNumber['ROUND_HALF_CEIL'] = 7;
BigNumber['ROUND_HALF_FLOOR'] = 8;

/*
 * Create an instance from a Buffer
 */
BigNumber['fromBuffer'] = function (buf, opts) {

    if (!opts) opts = {};

    var endian = { 1 : 'big', '-1' : 'little' }[opts.endian]
        || opts.endian || 'big'
    ;

    var size = opts.size === 'auto' ? Math.ceil(buf.length) : (opts.size || 1);

    if (buf.length % size !== 0) {
        throw new RangeError('Buffer length (' + buf.length + ')'
            + ' must be a multiple of size (' + size + ')'
        );
    }

    var hex = [];
    for (var i = 0; i < buf.length; i += size) {
        var chunk = [];
        for (var j = 0; j < size; j++) {
            chunk.push(buf[
                i + (endian === 'big' ? j : (size - j - 1))
            ]);
        }

        hex.push(chunk
            .map(function (c) {
                return (c < 16 ? '0' : '') + c.toString(16);
            })
            .join('')
        );
    }

    return BigNumber(hex.join(''), 16);

};

/*
 * Configure infrequently-changing library-wide settings.
 *
 * Accept an object or an argument list, with one or many of the following
 * properties or parameters respectively:
 * [ DECIMAL_PLACES [, ROUNDING_MODE [, EXPONENTIAL_AT [, RANGE [, ERRORS ]]]]]
 *
 * E.g.
 * BigNumber.config(20, 4) is equivalent to
 * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
 * Ignore properties/parameters set to null or undefined.
 *
 * Return an object with the properties current values.
 */
BigNumber['config'] = function () {
    var v, p,
        i = 0,
        r = {},
        a = arguments,
        o = a[0],
        c = 'config',
        inRange = function ( n, lo, hi ) {
          return !( ( outOfRange = n < lo || n > hi ) ||
            parse(n) != n && n !== 0 );
        },
        has = o && typeof o == 'object'
          ? function () {if ( o.hasOwnProperty(p) ) return ( v = o[p] ) != null}
          : function () {if ( a.length > i ) return ( v = a[i++] ) != null};

    // [DECIMAL_PLACES] {number} Integer, 0 to MAX inclusive.
    if ( has( p = 'DECIMAL_PLACES' ) ) {

        if ( inRange( v, 0, MAX ) ) {
            DECIMAL_PLACES = v | 0;
        } else {

            // 'config() DECIMAL_PLACES not an integer: {v}'
            // 'config() DECIMAL_PLACES out of range: {v}'
            ifExceptionsThrow( v, p, c );
        }
    }
    r[p] = DECIMAL_PLACES;

    // [ROUNDING_MODE] {number} Integer, 0 to 8 inclusive.
    if ( has( p = 'ROUNDING_MODE' ) ) {

        if ( inRange( v, 0, 8 ) ) {
            ROUNDING_MODE = v | 0;
        } else {

            // 'config() ROUNDING_MODE not an integer: {v}'
            // 'config() ROUNDING_MODE out of range: {v}'
            ifExceptionsThrow( v, p, c );
        }
    }
    r[p] = ROUNDING_MODE;

    /*
     * [EXPONENTIAL_AT] {number|number[]} Integer, -MAX to MAX inclusive or
     * [ integer -MAX to 0 inclusive, 0 to MAX inclusive ].
     */
    if ( has( p = 'EXPONENTIAL_AT' ) ) {

        if ( inRange( v, -MAX, MAX ) ) {
            TO_EXP_NEG = -( TO_EXP_POS = ~~( v < 0 ? -v : +v ) );
        } else if ( !outOfRange && v && inRange( v[0], -MAX, 0 ) &&
          inRange( v[1], 0, MAX ) ) {
            TO_EXP_NEG = ~~v[0];
            TO_EXP_POS = ~~v[1];
        } else {

            // 'config() EXPONENTIAL_AT not an integer or not [integer, integer]: {v}'
            // 'config() EXPONENTIAL_AT out of range or not [negative, positive: {v}'
            ifExceptionsThrow( v, p, c, 1 );
        }
    }
    r[p] = [ TO_EXP_NEG, TO_EXP_POS ];

    /*
     * [RANGE][ {number|number[]} Non-zero integer, -MAX to MAX inclusive or
     * [ integer -MAX to -1 inclusive, integer 1 to MAX inclusive ].
     */
    if ( has( p = 'RANGE' ) ) {

        if ( inRange( v, -MAX, MAX ) && ~~v ) {
            MIN_EXP = -( MAX_EXP = ~~( v < 0 ? -v : +v ) );
        } else if ( !outOfRange && v && inRange( v[0], -MAX, -1 ) &&
          inRange( v[1], 1, MAX ) ) {
            MIN_EXP = ~~v[0], MAX_EXP = ~~v[1];
        } else {

            // 'config() RANGE not a non-zero integer or not [integer, integer]: {v}'
            // 'config() RANGE out of range or not [negative, positive: {v}'
            ifExceptionsThrow( v, p, c, 1, 1 );
        }
    }
    r[p] = [ MIN_EXP, MAX_EXP ];

    // [ERRORS] {boolean|number} true, false, 1 or 0.
    if ( has( p = 'ERRORS' ) ) {

        if ( v === !!v || v === 1 || v === 0 ) {
            parse = ( outOfRange = id = 0, ERRORS = !!v )
              ? parseInt
              : parseFloat;
        } else {

            // 'config() ERRORS not a boolean or binary digit: {v}'
            ifExceptionsThrow( v, p, c, 0, 0, 1 );
        }
    }
    r[p] = ERRORS;

    return r;
};


// privated FUNCTIONS


// Assemble error messages. Throw BigNumber Errors.
function ifExceptionsThrow( arg, i, j, isArray, isRange, isErrors) {

    if ( ERRORS ) {
        var error,
            method = ['new BigNumber', 'cmp', 'div', 'eq', 'gt', 'gte', 'lt',
                 'lte', 'minus', 'mod', 'plus', 'times', 'toFr'
                ][ id ? id < 0 ? -id : id : 1 / id < 0 ? 1 : 0 ] + '()',
            message = outOfRange ? ' out of range' : ' not a' +
              ( isRange ? ' non-zero' : 'n' ) + ' integer';

        message = ( [
            method + ' number type has more than 15 significant digits',
            method + ' not a base ' + j + ' number',
            method + ' base' + message,
            method + ' not a number' ][i] ||
              j + '() ' + i + ( isErrors
                ? ' not a boolean or binary digit'
                : message + ( isArray
                  ? ' or not [' + ( outOfRange
                    ? ' negative, positive'
                    : ' integer, integer' ) + ' ]'
                  : '' ) ) ) + ': ' + arg;

        outOfRange = id = 0;
        error = new Error(message);
        error['name'] = 'BigNumber Error';

        throw error;
    }
}


/*
 * Convert a numeric string of baseIn to a numeric string of baseOut.
 */
function convert( nStr, baseOut, baseIn, sign ) {
    var e, dvs, dvd, nArr, fracArr, fracBN;

    // Convert string of base bIn to an array of numbers of baseOut.
    // Eg. strToArr('255', 10) where baseOut is 16, returns [15, 15].
    // Eg. strToArr('ff', 16)  where baseOut is 10, returns [2, 5, 5].
    function strToArr( str, bIn ) {
        var j,
            i = 0,
            strL = str.length,
            arrL,
            arr = [0];

        for ( bIn = bIn || baseIn; i < strL; i++ ) {

            for ( arrL = arr.length, j = 0; j < arrL; arr[j] *= bIn, j++ ) {
            }

            for ( arr[0] += DIGITS.indexOf( str.charAt(i) ), j = 0;
                  j < arr.length;
                  j++ ) {

                if ( arr[j] > baseOut - 1 ) {

                    if ( arr[j + 1] == null ) {
                        arr[j + 1] = 0;
                    }
                    arr[j + 1] += arr[j] / baseOut ^ 0;
                    arr[j] %= baseOut;
                }
            }
        }

        return arr.reverse();
    }

    // Convert array to string.
    // E.g. arrToStr( [9, 10, 11] ) becomes '9ab' (in bases above 11).
    function arrToStr( arr ) {
        var i = 0,
            arrL = arr.length,
            str = '';

        for ( ; i < arrL; str += DIGITS.charAt( arr[i++] ) ) {
        }

        return str;
    }

    if ( baseIn < 37 ) {
        nStr = nStr.toLowerCase();
    }

    /*
     * If non-integer convert integer part and fraction part separately.
     * Convert the fraction part as if it is an integer than use division to
     * reduce it down again to a value less than one.
     */
    if ( ( e = nStr.indexOf( '.' ) ) > -1 ) {

        /*
         * Calculate the power to which to raise the base to get the number
         * to divide the fraction part by after it has been converted as an
         * integer to the required base.
         */
        e = nStr.length - e - 1;

        // Use toFixed to avoid possible exponential notation.
        dvs = strToArr( new BigNumber(baseIn)['pow'](e)['toF'](), 10 );

        nArr = nStr.split('.');

        // Convert the base of the fraction part (as integer).
        dvd = strToArr( nArr[1] );

        // Convert the base of the integer part.
        nArr = strToArr( nArr[0] );

        // Result will be a BigNumber with a value less than 1.
        fracBN = divide( dvd, dvs, dvd.length - dvs.length, sign, baseOut,
          // Is least significant digit of integer part an odd number?
          nArr[nArr.length - 1] & 1 );

        fracArr = fracBN['c'];

        // e can be <= 0  ( if e == 0, fracArr is [0] or [1] ).
        if ( e = fracBN['e'] ) {

            // Append zeros according to the exponent of the result.
            for ( ; ++e; fracArr.unshift(0) ) {
            }

            // Append the fraction part to the converted integer part.
            nStr = arrToStr(nArr) + '.' + arrToStr(fracArr);

        // fracArr is [1].
        // Fraction digits rounded up, so increment last digit of integer part.
        } else if ( fracArr[0] ) {

            if ( nArr[ e = nArr.length - 1 ] < baseOut - 1 ) {
                ++nArr[e];
                nStr = arrToStr(nArr);
            } else {
                nStr = new BigNumber( arrToStr(nArr),
                  baseOut )['plus'](ONE)['toS'](baseOut);
            }

        // fracArr is [0]. No fraction digits.
        } else {
            nStr = arrToStr(nArr);
        }
    } else {

        // Simple integer. Convert base.
        nStr = arrToStr( strToArr(nStr) );
    }

    return nStr;
}


// Perform division in the specified base. Called by div and convert.
function divide( dvd, dvs, exp, s, base, isOdd ) {
    var dvsL, dvsT, next, cmp, remI,
        dvsZ = dvs.slice(),
        dvdI = dvsL = dvs.length,
        dvdL = dvd.length,
        rem = dvd.slice( 0, dvsL ),
        remL = rem.length,
        quo = new BigNumber(ONE),
        qc = quo['c'] = [],
        qi = 0,
        dig = DECIMAL_PLACES + ( quo['e'] = exp ) + 1;

    quo['s'] = s;
    s = dig < 0 ? 0 : dig;

    // Add zeros to make remainder as long as divisor.
    for ( ; remL++ < dvsL; rem.push(0) ) {
    }

    // Create version of divisor with leading zero.
    dvsZ.unshift(0);

    do {

        // 'next' is how many times the divisor goes into the current remainder.
        for ( next = 0; next < base; next++ ) {

            // Compare divisor and remainder.
            if ( dvsL != ( remL = rem.length ) ) {
                cmp = dvsL > remL ? 1 : -1;
            } else {
                for ( remI = -1, cmp = 0; ++remI < dvsL; ) {

                    if ( dvs[remI] != rem[remI] ) {
                        cmp = dvs[remI] > rem[remI] ? 1 : -1;
                        break;
                    }
                }
            }

            // Subtract divisor from remainder (if divisor < remainder).
            if ( cmp < 0 ) {

                // Remainder cannot be more than one digit longer than divisor.
                // Equalise lengths using divisor with extra leading zero?
                for ( dvsT = remL == dvsL ? dvs : dvsZ; remL; ) {

                    if ( rem[--remL] < dvsT[remL] ) {

                        for ( remI = remL;
                          remI && !rem[--remI];
                            rem[remI] = base - 1 ) {
                        }
                        --rem[remI];
                        rem[remL] += base;
                    }
                    rem[remL] -= dvsT[remL];
                }
                for ( ; !rem[0]; rem.shift() ) {
                }
            } else {
                break;
            }
        }

        // Add the 'next' digit to the result array.
        qc[qi++] = cmp ? next : ++next;

        // Update the remainder.
        rem[0] && cmp
          ? ( rem[remL] = dvd[dvdI] || 0 )
          : ( rem = [ dvd[dvdI] ] );

    } while ( ( dvdI++ < dvdL || rem[0] != null ) && s-- );

    // Leading zero? Do not remove if result is simply zero (qi == 1).
    if ( !qc[0] && qi != 1 ) {

        // There can't be more than one zero.
        --quo['e'];
        qc.shift();
    }

    // Round?
    if ( qi > dig ) {
        rnd( quo, DECIMAL_PLACES, base, isOdd, rem[0] != null );
    }

    // Overflow?
    if ( quo['e'] > MAX_EXP ) {

        // Infinity.
        quo['c'] = quo['e'] = null;

    // Underflow?
    } else if ( quo['e'] < MIN_EXP ) {

        // Zero.
        quo['c'] = [quo['e'] = 0];
    }

    return quo;
}


/*
 * Return a string representing the value of BigNumber n in normal or
 * exponential notation rounded to the specified decimal places or
 * significant digits.
 * Called by toString, toExponential (exp 1), toFixed, and toPrecision (exp 2).
 * d is the index (with the value in normal notation) of the digit that may be
 * rounded up.
 */
function format( n, d, exp ) {

    // Initially, i is the number of decimal places required.
    var i = d - (n = new BigNumber(n))['e'],
        c = n['c'];

    // +-Infinity or NaN?
    if ( !c ) {
        return n['toS']();
    }

    // Round?
    if ( c.length > ++d ) {
        rnd( n, i, 10 );
    }

    // Recalculate d if toFixed as n['e'] may have changed if value rounded up.
    i = c[0] == 0 ? i + 1 : exp ? d : n['e'] + i + 1;

    // Append zeros?
    for ( ; c.length < i; c.push(0) ) {
    }
    i = n['e'];

    /*
     * toPrecision returns exponential notation if the number of significant
     * digits specified is less than the number of digits necessary to
     * represent the integer part of the value in normal notation.
     */
    return exp == 1 || exp == 2 && ( --d < i || i <= TO_EXP_NEG )

      // Exponential notation.
      ? ( n['s'] < 0 && c[0] ? '-' : '' ) + ( c.length > 1
        ? ( c.splice( 1, 0, '.' ), c.join('') )
        : c[0] ) + ( i < 0 ? 'e' : 'e+' ) + i

      // Normal notation.
      : n['toS']();
}


// Round if necessary.
// Called by divide, format, setMode and sqrt.
function rnd( x, dp, base, isOdd, r ) {
    var xc = x['c'],
        isNeg = x['s'] < 0,
        half = base / 2,
        i = x['e'] + dp + 1,

        // 'next' is the digit after the digit that may be rounded up.
        next = xc[i],

        /*
         * 'more' is whether there are digits after 'next'.
         * E.g.
         * 0.005 (e = -3) to be rounded to 0 decimal places (dp = 0) gives i = -2
         * The 'next' digit is zero, and there ARE 'more' digits after it.
         * 0.5 (e = -1) dp = 0 gives i = 0
         * The 'next' digit is 5 and there are no 'more' digits after it.
         */
        more = r || i < 0 || xc[i + 1] != null;

    r = ROUNDING_MODE < 4
      ? ( next != null || more ) &&
        ( ROUNDING_MODE == 0 ||
           ROUNDING_MODE == 2 && !isNeg ||
             ROUNDING_MODE == 3 && isNeg )
      : next > half || next == half &&
        ( ROUNDING_MODE == 4 || more ||

          /*
           * isOdd is used in base conversion and refers to the least significant
           * digit of the integer part of the value to be converted. The fraction
           * part is rounded by this method separately from the integer part.
           */
          ROUNDING_MODE == 6 && ( xc[i - 1] & 1 || !dp && isOdd ) ||
            ROUNDING_MODE == 7 && !isNeg ||
              ROUNDING_MODE == 8 && isNeg );

    if ( i < 1 || !xc[0] ) {
        xc.length = 0;
        xc.push(0);

        if ( r ) {

            // 1, 0.1, 0.01, 0.001, 0.0001 etc.
            xc[0] = 1;
            x['e'] = -dp;
        } else {

            // Zero.
            x['e'] = 0;
        }

        return x;
    }

    // Remove any digits after the required decimal places.
    xc.length = i--;

    // Round up?
    if ( r ) {

        // Rounding up may mean the previous digit has to be rounded up and so on.
        for ( --base; ++xc[i] > base; ) {
            xc[i] = 0;

            if ( !i-- ) {
                ++x['e'];
                xc.unshift(1);
            }
        }
    }

    // Remove trailing zeros.
    for ( i = xc.length; !xc[--i]; xc.pop() ) {
    }

    return x;
}


// Round after setting the appropriate rounding mode.
// Handles ceil, floor and round.
function setMode( x, dp, rm ) {
    var r = ROUNDING_MODE;

    ROUNDING_MODE = rm;
    x = new BigNumber(x);
    x['c'] && rnd( x, dp, 10 );
    ROUNDING_MODE = r;

    return x;
}


// PROTOTYPE/INSTANCE METHODS


/*
 * Return a new BigNumber whose value is the absolute value of this BigNumber.
 */
P['abs'] = P['absoluteValue'] = function () {
    var x = new BigNumber(this);

    if ( x['s'] < 0 ) {
        x['s'] = 1;
    }

    return x;
};

/*
 * Return the bit length of the number.
 */
P['bitLength'] = function () {
    return this.toString(2).length;
};


/*
 * Return a new BigNumber whose value is the value of this BigNumber
 * rounded to a whole number in the direction of Infinity.
 */
P['ceil'] = function () {
    return setMode( this, 0, 2 );
};


/*
 * Return
 * 1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
 * -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
 * 0 if they have the same value,
 * or null if the value of either is NaN.
 */
P['comparedTo'] = P['cmp'] = function ( y, b ) {
    var a,
        x = this,
        xc = x['c'],
        yc = ( id = -id, y = new BigNumber( y, b ) )['c'],
        i = x['s'],
        j = y['s'],
        k = x['e'],
        l = y['e'];

    // Either NaN?
    if ( !i || !j ) {
        return null;
    }

    a = xc && !xc[0], b = yc && !yc[0];

    // Either zero?
    if ( a || b ) {
        return a ? b ? 0 : -j : i;
    }

    // Signs differ?
    if ( i != j ) {
        return i;
    }

    // Either Infinity?
    if ( a = i < 0, b = k == l, !xc || !yc ) {
        return b ? 0 : !xc ^ a ? 1 : -1;
    }

    // Compare exponents.
    if ( !b ) {
        return k > l ^ a ? 1 : -1;
    }

    // Compare digit by digit.
    for ( i = -1,
          j = ( k = xc.length ) < ( l = yc.length ) ? k : l;
          ++i < j; ) {

        if ( xc[i] != yc[i] ) {
            return xc[i] > yc[i] ^ a ? 1 : -1;
        }
    }
    // Compare lengths.
    return k == l ? 0 : k > l ^ a ? 1 : -1;
};


/*
 *  n / 0 = I
 *  n / N = N
 *  n / I = 0
 *  0 / n = 0
 *  0 / 0 = N
 *  0 / N = N
 *  0 / I = 0
 *  N / n = N
 *  N / 0 = N
 *  N / N = N
 *  N / I = N
 *  I / n = I
 *  I / 0 = I
 *  I / N = N
 *  I / I = N
 *
 * Return a new BigNumber whose value is the value of this BigNumber
 * divided by the value of BigNumber(y, b), rounded according to
 * DECIMAL_PLACES and ROUNDING_MODE.
 */
P['dividedBy'] = P['div'] = function ( y, b ) {
    var xc = this['c'],
        xe = this['e'],
        xs = this['s'],
        yc = ( id = 2, y = new BigNumber( y, b ) )['c'],
        ye = y['e'],
        ys = y['s'],
        s = xs == ys ? 1 : -1;

    // Either NaN/Infinity/0?
    return !xe && ( !xc || !xc[0] ) || !ye && ( !yc || !yc[0] )

      // Either NaN?
      ? new BigNumber( !xs || !ys ||

        // Both 0 or both Infinity?
        ( xc ? yc && xc[0] == yc[0] : !yc )

          // Return NaN.
          ? NaN

          // x is 0 or y is Infinity?
          : xc && xc[0] == 0 || !yc

            // Return +-0.
            ? s * 0

            // y is 0. Return +-Infinity.
            : s / 0 )

      : divide( xc, yc, xe - ye, s, 10 );
};


/*
 * Return true if the value of this BigNumber is equal to the value of
 * BigNumber(n, b), otherwise returns false.
 */
P['equals'] = P['eq'] = function ( n, b ) {
    id = 3;
    return this['cmp']( n, b ) === 0;
};


/*
 * Return a new BigNumber whose value is the value of this BigNumber
 * rounded to a whole number in the direction of -Infinity.
 */
P['floor'] = function () {
    return setMode( this, 0, 3 );
};


/*
 * Return true if the value of this BigNumber is greater than the value of
 * BigNumber(n, b), otherwise returns false.
 */
P['greaterThan'] = P['gt'] = function ( n, b ) {
    id = 4;
    return this['cmp']( n, b ) > 0;
};


/*
 * Return true if the value of this BigNumber is greater than or equal to
 * the value of BigNumber(n, b), otherwise returns false.
 */
P['greaterThanOrEqualTo'] = P['gte'] = function ( n, b ) {
    id = 5;
    return ( b = this['cmp']( n, b ) ) == 1 || b === 0;
};


/*
 * Return true if the value of this BigNumber is a finite number, otherwise
 * returns false.
 */
P['isFinite'] = P['isF'] = function () {
    return !!this['c'];
};


/*
 * Return true if the value of this BigNumber is NaN, otherwise returns
 * false.
 */
P['isNaN'] = function () {
    return !this['s'];
};


/*
 * Return true if the value of this BigNumber is negative, otherwise
 * returns false.
 */
P['isNegative'] = P['isNeg'] = function () {
    return this['s'] < 0;
};


/*
 * Return true if the value of this BigNumber is 0 or -0, otherwise returns
 * false.
 */
P['isZero'] = P['isZ'] = function () {
    return !!this['c'] && this['c'][0] == 0;
};


/*
 * Return true if the value of this BigNumber is less than the value of
 * BigNumber(n, b), otherwise returns false.
 */
P['lessThan'] = P['lt'] = function ( n, b ) {
    id = 6;
    return this['cmp']( n, b ) < 0;
};


/*
 * Return true if the value of this BigNumber is less than or equal to the
 * value of BigNumber(n, b), otherwise returns false.
 */
P['lessThanOrEqualTo'] = P['lte'] = P['le'] = function ( n, b ) {
    id = 7;
    return ( b = this['cmp']( n, b ) ) == -1 || b === 0;
};


/*
 *  n - 0 = n
 *  n - N = N
 *  n - I = -I
 *  0 - n = -n
 *  0 - 0 = 0
 *  0 - N = N
 *  0 - I = -I
 *  N - n = N
 *  N - 0 = N
 *  N - N = N
 *  N - I = N
 *  I - n = I
 *  I - 0 = I
 *  I - N = N
 *  I - I = N
 *
 * Return a new BigNumber whose value is the value of this BigNumber minus
 * the value of BigNumber(y, b).
 */
P['minus'] = P['sub'] = function ( y, b ) {
    var d, i, j, xLTy,
        x = this,
        a = x['s'];

    b = ( id = 8, y = new BigNumber( y, b ) )['s'];

    // Either NaN?
    if ( !a || !b ) {
        return new BigNumber(NaN);
    }

    // Signs differ?
    if ( a != b ) {
        return y['s'] = -b, x['plus'](y);
    }

    var xc = x['c'],
        xe = x['e'],
        yc = y['c'],
        ye = y['e'];

    if ( !xe || !ye ) {

        // Either Infinity?
        if ( !xc || !yc ) {
            return xc ? ( y['s'] = -b, y ) : new BigNumber( yc ? x : NaN );
        }

        // Either zero?
        if ( !xc[0] || !yc[0] ) {

            // y is non-zero?
            return yc[0]
              ? ( y['s'] = -b, y )

              // x is non-zero?
              : new BigNumber( xc[0]
                ? x

                // Both are zero.
                // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
                : ROUNDING_MODE == 3 ? -0 : 0 );
        }
    }

    // Determine which is the bigger number.
    // Prepend zeros to equalise exponents.
    if ( xc = xc.slice(), a = xe - ye ) {
        d = ( xLTy = a < 0 ) ? ( a = -a, xc ) : ( ye = xe, yc );

        for ( d.reverse(), b = a; b--; d.push(0) ) {
        }
        d.reverse();
    } else {

        // Exponents equal. Check digit by digit.
        j = ( ( xLTy = xc.length < yc.length ) ? xc : yc ).length;

        for ( a = b = 0; b < j; b++ ) {

            if ( xc[b] != yc[b] ) {
                xLTy = xc[b] < yc[b];
                break;
            }
        }
    }

    // x < y? Point xc to the array of the bigger number.
    if ( xLTy ) {
        d = xc, xc = yc, yc = d;
        y['s'] = -y['s'];
    }

    /*
     * Append zeros to xc if shorter. No need to add zeros to yc if shorter
     * as subtraction only needs to start at yc.length.
     */
    if ( ( b = -( ( j = xc.length ) - yc.length ) ) > 0 ) {

        for ( ; b--; xc[j++] = 0 ) {
        }
    }

    // Subtract yc from xc.
    for ( b = yc.length; b > a; ){

        if ( xc[--b] < yc[b] ) {

            for ( i = b; i && !xc[--i]; xc[i] = 9 ) {
            }
            --xc[i];
            xc[b] += 10;
        }
        xc[b] -= yc[b];
    }

    // Remove trailing zeros.
    for ( ; xc[--j] == 0; xc.pop() ) {
    }

    // Remove leading zeros and adjust exponent accordingly.
    for ( ; xc[0] == 0; xc.shift(), --ye ) {
    }

    /*
     * No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
     * when neither x or y are Infinity.
     */

    // Underflow?
    if ( ye < MIN_EXP || !xc[0] ) {

        /*
         * Following IEEE 754 (2008) 6.3,
         * n - n = +0  but  n - n = -0 when rounding towards -Infinity.
         */
        if ( !xc[0] ) {
            y['s'] = ROUNDING_MODE == 3 ? -1 : 1;
        }

        // Result is zero.
        xc = [ye = 0];
    }

    return y['c'] = xc, y['e'] = ye, y;
};


/*
 *   n % 0 =  N
 *   n % N =  N
 *   0 % n =  0
 *  -0 % n = -0
 *   0 % 0 =  N
 *   0 % N =  N
 *   N % n =  N
 *   N % 0 =  N
 *   N % N =  N
 *
 * Return a new BigNumber whose value is the value of this BigNumber modulo
 * the value of BigNumber(y, b).
 */
P['modulo'] = P['mod'] = function ( y, b ) {
    var x = this,
        xc = x['c'],
        yc = ( id = 9, y = new BigNumber( y, b ) )['c'],
        i = x['s'],
        j = y['s'];

    // Is x or y NaN, or y zero?
    b = !i || !j || yc && !yc[0];

    if ( b || xc && !xc[0] ) {
        return new BigNumber( b ? NaN : x );
    }

    x['s'] = y['s'] = 1;
    b = y['cmp'](x) == 1;
    x['s'] = i, y['s'] = j;

    return b
      ? new BigNumber(x)
      : ( i = DECIMAL_PLACES, j = ROUNDING_MODE,
        DECIMAL_PLACES = 0, ROUNDING_MODE = 1,
          x = x['div'](y),
            DECIMAL_PLACES = i, ROUNDING_MODE = j,
              this['minus']( x['times'](y) ) );
};


/*
 * Return a new BigNumber whose value is the value of this BigNumber
 * negated, i.e. multiplied by -1.
 */
P['negated'] = P['neg'] = function () {
    var x = new BigNumber(this);

    return x['s'] = -x['s'] || null, x;
};


/*
 *  n + 0 = n
 *  n + N = N
 *  n + I = I
 *  0 + n = n
 *  0 + 0 = 0
 *  0 + N = N
 *  0 + I = I
 *  N + n = N
 *  N + 0 = N
 *  N + N = N
 *  N + I = N
 *  I + n = I
 *  I + 0 = I
 *  I + N = N
 *  I + I = I
 *
 * Return a new BigNumber whose value is the value of this BigNumber plus
 * the value of BigNumber(y, b).
 */
P['plus'] = P['add'] = function ( y, b ) {
    var d,
        x = this,
        a = x['s'];

    b = ( id = 10, y = new BigNumber( y, b ) )['s'];

    // Either NaN?
    if ( !a || !b ) {
        return new BigNumber(NaN);
    }

    // Signs differ?
    if ( a != b ) {
        return y['s'] = -b, x['minus'](y);
    }

    var xe = x['e'],
        xc = x['c'],
        ye = y['e'],
        yc = y['c'];

    if ( !xe || !ye ) {

        // Either Infinity?
        if ( !xc || !yc ) {

            // Return +-Infinity.
            return new BigNumber( a / 0 );
        }

        // Either zero?
        if ( !xc[0] || !yc[0] ) {

            // y is non-zero?
            return yc[0]
              ? y

              // x is non-zero?
              : new BigNumber( xc[0]
                ? x

                // Both are zero. Return zero.
                : a * 0 );
        }
    }

    // Prepend zeros to equalise exponents.
    // Note: Faster to use reverse then do unshifts.
    if ( xc = xc.slice(), a = xe - ye ) {
        d = a > 0 ? ( ye = xe, yc ) : ( a = -a, xc );

        for ( d.reverse(); a--; d.push(0) ) {
        }
        d.reverse();
    }

    // Point xc to the longer array.
    if ( xc.length - yc.length < 0 ) {
        d = yc, yc = xc, xc = d;
    }

    /*
     * Only start adding at yc.length - 1 as the
     * further digits of xc can be left as they are.
     */
    for ( a = yc.length, b = 0; a;
         b = ( xc[--a] = xc[a] + yc[a] + b ) / 10 ^ 0, xc[a] %= 10 ) {
    }

    // No need to check for zero, as +x + +y != 0 && -x + -y != 0

    if ( b ) {
        xc.unshift(b);

        // Overflow? (MAX_EXP + 1 possible)
        if ( ++ye > MAX_EXP ) {

            // Infinity.
            xc = ye = null;
        }
    }

     // Remove trailing zeros.
    for ( a = xc.length; xc[--a] == 0; xc.pop() ) {
    }

    return y['c'] = xc, y['e'] = ye, y;
};


/*
 * Return a BigNumber whose value is the value of this BigNumber raised to
 * the power e. If e is negative round according to DECIMAL_PLACES and
 * ROUNDING_MODE.
 *
 * e {number} Integer, -MAX_POWER to MAX_POWER inclusive.
 */
P['toPower'] = P['pow'] = function ( e ) {

    // e to integer, avoiding NaN or Infinity becoming 0.
    var i = e * 0 == 0 ? e | 0 : e,
        x = new BigNumber(this),
        y = new BigNumber(ONE);

    // Use Math.pow?
    // Pass +-Infinity for out of range exponents.
    if ( ( ( ( outOfRange = e < -MAX_POWER || e > MAX_POWER ) &&
      (i = e * 1 / 0) ) ||

         /*
          * Any exponent that fails the parse becomes NaN.
          *
          * Include 'e !== 0' because on Opera -0 == parseFloat(-0) is false,
          * despite -0 === parseFloat(-0) && -0 == parseFloat('-0') is true.
          */
         parse(e) != e && e !== 0 && !(i = NaN) ) &&

          // 'pow() exponent not an integer: {e}'
          // 'pow() exponent out of range: {e}'
          !ifExceptionsThrow( e, 'exponent', 'pow' ) ||

            // Pass zero to Math.pow, as any value to the power zero is 1.
            !i ) {

        // i is +-Infinity, NaN or 0.
        return new BigNumber( Math.pow( x['toS'](), i ) );
    }

    for ( i = i < 0 ? -i : i; ; ) {

        if ( i & 1 ) {
            y = y['times'](x);
        }
        i >>= 1;

        if ( !i ) {
            break;
        }
        x = x['times'](x);
    }

    return e < 0 ? ONE['div'](y) : y;
};


/*
 * Return a BigNumber whose value is the value of this BigNumber raised to
 * the power m modulo n.
 *
 * m {BigNumber} the value to take the power of
 * n {BigNumber} the value to modulo by
 */
P['powm'] = function ( m, n ) {
    return this.pow(m).mod(n);
};


/*
 * Return a new BigNumber whose value is the value of this BigNumber
 * rounded to a maximum of dp decimal places using rounding mode rm, or to
 * 0 and ROUNDING_MODE respectively if omitted.
 *
 * [dp] {number} Integer, 0 to MAX inclusive.
 * [rm] {number} Integer, 0 to 8 inclusive.
 */
P['round'] = function ( dp, rm ) {

    dp = dp == null || ( ( ( outOfRange = dp < 0 || dp > MAX ) ||
      parse(dp) != dp ) &&

        // 'round() decimal places out of range: {dp}'
        // 'round() decimal places not an integer: {dp}'
        !ifExceptionsThrow( dp, 'decimal places', 'round' ) )
          ? 0
          : dp | 0;

    rm = rm == null || ( ( ( outOfRange = rm < 0 || rm > 8 ) ||

      // Include '&& rm !== 0' because with Opera -0 == parseFloat(-0) is false.
      parse(rm) != rm && rm !== 0 ) &&

        // 'round() mode not an integer: {rm}'
        // 'round() mode out of range: {rm}'
        !ifExceptionsThrow( rm, 'mode', 'round' ) )
          ? ROUNDING_MODE
          : rm | 0;

    return setMode( this, dp, rm );
};


/*
 *  sqrt(-n) =  N
 *  sqrt( N) =  N
 *  sqrt(-I) =  N
 *  sqrt( I) =  I
 *  sqrt( 0) =  0
 *  sqrt(-0) = -0
 *
 * Return a new BigNumber whose value is the square root of the value of
 * this BigNumber, rounded according to DECIMAL_PLACES and ROUNDING_MODE.
 */
P['squareRoot'] = P['sqrt'] = function () {
    var n, r, re, t,
        x = this,
        c = x['c'],
        s = x['s'],
        e = x['e'],
        dp = DECIMAL_PLACES,
        rm = ROUNDING_MODE,
        half = new BigNumber('0.5');

    // Negative/NaN/Infinity/zero?
    if ( s !== 1 || !c || !c[0] ) {

        return new BigNumber( !s || s < 0 && ( !c || c[0] )
          ? NaN
          : c ? x : 1 / 0 );
    }

    // Initial estimate.
    s = Math.sqrt( x['toS']() );
    ROUNDING_MODE = 1;

    /*
      Math.sqrt underflow/overflow?
      Pass x to Math.sqrt as integer, then adjust the exponent of the result.
     */
    if ( s == 0 || s == 1 / 0 ) {
        n = c.join('');

        if ( !( n.length + e & 1 ) ) {
            n += '0';
        }
        r = new BigNumber( Math.sqrt(n) + '' );

        // r may still not be finite.
        if ( !r['c'] ) {
            r['c'] = [1];
        }
        r['e'] = ( ( ( e + 1 ) / 2 ) | 0 ) - ( e < 0 || e & 1 );
    } else {
        r = new BigNumber( n = s.toString() );
    }
    re = r['e'];
    s = re + ( DECIMAL_PLACES += 4 );

    if ( s < 3 ) {
        s = 0;
    }
    e = s;

    // Newton-Raphson iteration.
    for ( ; ; ) {
        t = r;
        r = half['times']( t['plus']( x['div'](t) ) );

        if ( t['c'].slice( 0, s ).join('') === r['c'].slice( 0, s ).join('') ) {
            c = r['c'];

            /*
              The exponent of r may here be one less than the final result
              exponent (re), e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust
              s so the rounding digits are indexed correctly.
             */
            s = s - ( n && r['e'] < re );

            /*
              The 4th rounding digit may be in error by -1 so if the 4 rounding
              digits are 9999 or 4999 (i.e. approaching a rounding boundary)
              continue the iteration.
             */
            if ( c[s] == 9 && c[s - 1] == 9 && c[s - 2] == 9 &&
                    ( c[s - 3] == 9 || n && c[s - 3] == 4 ) ) {

                /*
                  If 9999 on first run through, check to see if rounding up
                  gives the exact result as the nines may infinitely repeat.
                 */
                if ( n && c[s - 3] == 9 ) {
                    t = r['round']( dp, 0 );

                    if ( t['times'](t)['eq'](x) ) {
                        ROUNDING_MODE = rm;
                        DECIMAL_PLACES = dp;

                        return t;
                    }
                }
                DECIMAL_PLACES += 4;
                s += 4;
                n = '';
            } else {

                /*
                  If the rounding digits are null, 0000 or 5000, check for an
                  exact result. If not, then there are further digits so
                  increment the 1st rounding digit to ensure correct rounding.
                 */
                if ( !c[e] && !c[e - 1] && !c[e - 2] &&
                        ( !c[e - 3] || c[e - 3] == 5 ) ) {

                    // Truncate to the first rounding digit.
                    if ( c.length > e - 2 ) {
                        c.length = e - 2;
                    }

                    if ( !r['times'](r)['eq'](x) ) {

                        while ( c.length < e - 3 ) {
                            c.push(0);
                        }
                        c[e - 3]++;
                    }
                }
                ROUNDING_MODE = rm;
                rnd( r, DECIMAL_PLACES = dp, 10 );

                return r;
            }
        }
    }
};


/*
 *  n * 0 = 0
 *  n * N = N
 *  n * I = I
 *  0 * n = 0
 *  0 * 0 = 0
 *  0 * N = N
 *  0 * I = N
 *  N * n = N
 *  N * 0 = N
 *  N * N = N
 *  N * I = N
 *  I * n = I
 *  I * 0 = N
 *  I * N = N
 *  I * I = I
 *
 * Return a new BigNumber whose value is the value of this BigNumber times
 * the value of BigNumber(y, b).
 */
P['times'] = P['mul'] = function ( y, b ) {
    var c,
        x = this,
        xc = x['c'],
        yc = ( id = 11, y = new BigNumber( y, b ) )['c'],
        i = x['e'],
        j = y['e'],
        a = x['s'];

    y['s'] = a == ( b = y['s'] ) ? 1 : -1;

    // Either NaN/Infinity/0?
    if ( !i && ( !xc || !xc[0] ) || !j && ( !yc || !yc[0] ) ) {

        // Either NaN?
        return new BigNumber( !a || !b ||

          // x is 0 and y is Infinity  or  y is 0 and x is Infinity?
          xc && !xc[0] && !yc || yc && !yc[0] && !xc

            // Return NaN.
            ? NaN

            // Either Infinity?
            : !xc || !yc

              // Return +-Infinity.
              ? y['s'] / 0

              // x or y is 0. Return +-0.
              : y['s'] * 0 );
    }
    y['e'] = i + j;

    if ( ( a = xc.length ) < ( b = yc.length ) ) {
        c = xc, xc = yc, yc = c, j = a, a = b, b = j;
    }

    for ( j = a + b, c = []; j--; c.push(0) ) {
    }

    // Multiply!
    for ( i = b - 1; i > -1; i-- ) {

        for ( b = 0, j = a + i;
              j > i;
              b = c[j] + yc[i] * xc[j - i - 1] + b,
              c[j--] = b % 10 | 0,
              b = b / 10 | 0 ) {
        }

        if ( b ) {
            c[j] = ( c[j] + b ) % 10;
        }
    }

    b && ++y['e'];

    // Remove any leading zero.
    !c[0] && c.shift();

    // Remove trailing zeros.
    for ( j = c.length; !c[--j]; c.pop() ) {
    }

    // No zero check needed as only x * 0 == 0 etc.

    // Overflow?
    y['c'] = y['e'] > MAX_EXP

      // Infinity.
      ? ( y['e'] = null )

      // Underflow?
      : y['e'] < MIN_EXP

        // Zero.
        ? [ y['e'] = 0 ]

        // Neither.
        : c;

    return y;
};

/*
 * Return a buffer containing the
 */
P['toBuffer'] = function ( opts ) {

    if (typeof opts === 'string') {
        if (opts !== 'mpint') return 'Unsupported Buffer representation';

        var abs = this.abs();
        var buf = abs.toBuffer({ size : 1, endian : 'big' });
        var len = buf.length === 1 && buf[0] === 0 ? 0 : buf.length;
        if (buf[0] & 0x80) len ++;

        var ret = new Buffer(4 + len);
        if (len > 0) buf.copy(ret, 4 + (buf[0] & 0x80 ? 1 : 0));
        if (buf[0] & 0x80) ret[4] = 0;

        ret[0] = len & (0xff << 24);
        ret[1] = len & (0xff << 16);
        ret[2] = len & (0xff << 8);
        ret[3] = len & (0xff << 0);

        // two's compliment for negative integers:
        var isNeg = this.lt(0);
        if (isNeg) {
            for (var i = 4; i < ret.length; i++) {
                ret[i] = 0xff - ret[i];
            }
        }
        ret[4] = (ret[4] & 0x7f) | (isNeg ? 0x80 : 0);
        if (isNeg) ret[ret.length - 1] ++;

        return ret;
    }

    if (!opts) opts = {};

    var endian = { 1 : 'big', '-1' : 'little' }[opts.endian]
        || opts.endian || 'big'
    ;

    var hex = this.toString(16);
    if (hex.charAt(0) === '-') throw new Error(
        'converting negative numbers to Buffers not supported yet'
    );

    var size = opts.size === 'auto' ? Math.ceil(hex.length / 2) : (opts.size || 1);

    var len = Math.ceil(hex.length / (2 * size)) * size;
    var buf = new Buffer(len);

    // zero-pad the hex string so the chunks are all `size` long
    while (hex.length < 2 * len) hex = '0' + hex;

    var hx = hex
        .split(new RegExp('(.{' + (2 * size) + '})'))
        .filter(function (s) { return s.length > 0 })
    ;

    hx.forEach(function (chunk, i) {
        for (var j = 0; j < size; j++) {
            var ix = i * size + (endian === 'big' ? j : size - j - 1);
            buf[ix] = parseInt(chunk.slice(j*2,j*2+2), 16);
        }
    });

    return buf;
};

/*
 * Return a string representing the value of this BigNumber in exponential
 * notation to dp fixed decimal places and rounded using ROUNDING_MODE if
 * necessary.
 *
 * [dp] {number} Integer, 0 to MAX inclusive.
 */
P['toExponential'] = P['toE'] = function ( dp ) {

    return format( this,
      ( dp == null || ( ( outOfRange = dp < 0 || dp > MAX ) ||

        /*
         * Include '&& dp !== 0' because with Opera -0 == parseFloat(-0) is
         * false, despite -0 == parseFloat('-0') && 0 == -0 being true.
         */
        parse(dp) != dp && dp !== 0 ) &&

          // 'toE() decimal places not an integer: {dp}'
          // 'toE() decimal places out of range: {dp}'
          !ifExceptionsThrow( dp, 'decimal places', 'toE' ) ) && this['c']
            ? this['c'].length - 1
            : dp | 0, 1 );
};


/*
 * Return a string representing the value of this BigNumber in normal
 * notation to dp fixed decimal places and rounded using ROUNDING_MODE if
 * necessary.
 *
 * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
 * but e.g. (-0.00001).toFixed(0) is '-0'.
 *
 * [dp] {number} Integer, 0 to MAX inclusive.
 */
P['toFixed'] = P['toF'] = function ( dp ) {
    var n, str, d,
        x = this;

    if ( !( dp == null || ( ( outOfRange = dp < 0 || dp > MAX ) ||
        parse(dp) != dp && dp !== 0 ) &&

        // 'toF() decimal places not an integer: {dp}'
        // 'toF() decimal places out of range: {dp}'
        !ifExceptionsThrow( dp, 'decimal places', 'toF' ) ) ) {
          d = x['e'] + ( dp | 0 );
    }

    n = TO_EXP_NEG, dp = TO_EXP_POS;
    TO_EXP_NEG = -( TO_EXP_POS = 1 / 0 );

    // Note: str is initially undefined.
    if ( d == str ) {
        str = x['toS']();
    } else {
        str = format( x, d );

        // (-0).toFixed() is '0', but (-0.1).toFixed() is '-0'.
        // (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
        if ( x['s'] < 0 && x['c'] ) {

            // As e.g. -0 toFixed(3), will wrongly be returned as -0.000 from toString.
            if ( !x['c'][0] ) {
                str = str.replace(/^-/, '');

            // As e.g. -0.5 if rounded to -0 will cause toString to omit the minus sign.
            } else if ( str.indexOf('-') < 0 ) {
                str = '-' + str;
            }
        }
    }
    TO_EXP_NEG = n, TO_EXP_POS = dp;

    return str;
};


/*
 * Return a string array representing the value of this BigNumber as a
 * simple fraction with an integer numerator and an integer denominator.
 * The denominator will be a positive non-zero value less than or equal to
 * the specified maximum denominator. If a maximum denominator is not
 * specified, the denominator will be the lowest value necessary to
 * represent the number exactly.
 *
 * [maxD] {number|string|BigNumber} Integer >= 1 and < Infinity.
 */
P['toFraction'] = P['toFr'] = function ( maxD ) {
    var q, frac, n0, d0, d2, n, e,
        n1 = d0 = new BigNumber(ONE),
        d1 = n0 = new BigNumber('0'),
        x = this,
        xc = x['c'],
        exp = MAX_EXP,
        dp = DECIMAL_PLACES,
        rm = ROUNDING_MODE,
        d = new BigNumber(ONE);

    // NaN, Infinity.
    if ( !xc ) {
        return x['toS']();
    }

    e = d['e'] = xc.length - x['e'] - 1;

    // If max denominator is undefined or null...
    if ( maxD == null ||

         // or NaN...
         ( !( id = 12, n = new BigNumber(maxD) )['s'] ||

           // or less than 1, or Infinity...
           ( outOfRange = n['cmp'](n1) < 0 || !n['c'] ) ||

             // or not an integer...
             ( ERRORS && n['e'] < n['c'].length - 1 ) ) &&

               // 'toFr() max denominator not an integer: {maxD}'
               // 'toFr() max denominator out of range: {maxD}'
               !ifExceptionsThrow( maxD, 'max denominator', 'toFr' ) ||

                 // or greater than the maxD needed to specify the value exactly...
                 ( maxD = n )['cmp'](d) > 0 ) {

        // d is e.g. 10, 100, 1000, 10000... , n1 is 1.
        maxD = e > 0 ? d : n1;
    }

    MAX_EXP = 1 / 0;
    n = new BigNumber( xc.join('') );

    for ( DECIMAL_PLACES = 0, ROUNDING_MODE = 1; ; )  {
        q = n['div'](d);
        d2 = d0['plus']( q['times'](d1) );

        if ( d2['cmp'](maxD) == 1 ) {
            break;
        }

        d0 = d1, d1 = d2;

        n1 = n0['plus']( q['times']( d2 = n1 ) );
        n0 = d2;

        d = n['minus']( q['times']( d2 = d ) );
        n = d2;
    }

    d2 = maxD['minus'](d0)['div'](d1);
    n0 = n0['plus']( d2['times'](n1) );
    d0 = d0['plus']( d2['times'](d1) );

    n0['s'] = n1['s'] = x['s'];

    DECIMAL_PLACES = e * 2;
    ROUNDING_MODE = rm;

    // Determine which fraction is closer to x, n0 / d0 or n1 / d1?
    frac = n1['div'](d1)['minus'](x)['abs']()['cmp'](
      n0['div'](d0)['minus'](x)['abs']() ) < 1
      ? [ n1['toS'](), d1['toS']() ]
      : [ n0['toS'](), d0['toS']() ];

    return MAX_EXP = exp, DECIMAL_PLACES = dp, frac;
};


/*
 * Return a string representing the value of this BigNumber to sd significant
 * digits and rounded using ROUNDING_MODE if necessary.
 * If sd is less than the number of digits necessary to represent the integer
 * part of the value in normal notation, then use exponential notation.
 *
 * sd {number} Integer, 1 to MAX inclusive.
 */
P['toPrecision'] = P['toP'] = function ( sd ) {

    /*
     * ERRORS true: Throw if sd not undefined, null or an integer in range.
     * ERRORS false: Ignore sd if not a number or not in range.
     * Truncate non-integers.
     */
    return sd == null || ( ( ( outOfRange = sd < 1 || sd > MAX ) ||
      parse(sd) != sd ) &&

        // 'toP() precision not an integer: {sd}'
        // 'toP() precision out of range: {sd}'
        !ifExceptionsThrow( sd, 'precision', 'toP' ) )
          ? this['toS']()
          : format( this, --sd | 0, 2 );
};


/*
 * Return a string representing the value of this BigNumber in base b, or
 * base 10 if b is omitted. If a base is specified, including base 10,
 * round according to DECIMAL_PLACES and ROUNDING_MODE.
 * If a base is not specified, and this BigNumber has a positive exponent
 * that is equal to or greater than TO_EXP_POS, or a negative exponent equal
 * to or less than TO_EXP_NEG, return exponential notation.
 *
 * [b] {number} Integer, 2 to 64 inclusive.
 */
P['toString'] = P['toS'] = function ( b ) {
    var u, str, strL,
        x = this,
        xe = x['e'];

    // Infinity or NaN?
    if ( xe === null ) {
        str = x['s'] ? 'Infinity' : 'NaN';

    // Exponential format?
    } else if ( b === u && ( xe <= TO_EXP_NEG || xe >= TO_EXP_POS ) ) {
        return format( x, x['c'].length - 1, 1 );
    } else {
        str = x['c'].join('');

        // Negative exponent?
        if ( xe < 0 ) {

            // Prepend zeros.
            for ( ; ++xe; str = '0' + str ) {
            }
            str = '0.' + str;

        // Positive exponent?
        } else if ( strL = str.length, xe > 0 ) {

            if ( ++xe > strL ) {

                // Append zeros.
                for ( xe -= strL; xe-- ; str += '0' ) {
                }
            } else if ( xe < strL ) {
                str = str.slice( 0, xe ) + '.' + str.slice(xe);
            }

        // Exponent zero.
        } else {
            if ( u = str.charAt(0), strL > 1 ) {
                str = u + '.' + str.slice(1);

            // Avoid '-0'
            } else if ( u == '0' ) {
                return u;
            }
        }

        if ( b != null ) {

            if ( !( outOfRange = !( b >= 2 && b < 65 ) ) &&
              ( b == (b | 0) || !ERRORS ) ) {
                str = convert( str, b | 0, 10, x['s'] );

                // Avoid '-0'
                if ( str == '0' ) {
                    return str;
                }
            } else {

                // 'toS() base not an integer: {b}'
                // 'toS() base out of range: {b}'
                ifExceptionsThrow( b, 'base', 'toS' );
            }
        }

    }

    return x['s'] < 0 ? '-' + str : str;
};

P['toNumber'] = function () {
  return parseInt(this['toString'](), 10);
};


/*
 * Return as toString, but do not accept a base argument.
 */
P['valueOf'] = function () {
    return this['toS']();
};


// Add aliases for BigDecimal methods.
//P['add'] = P['plus'];
//P['subtract'] = P['minus'];
//P['multiply'] = P['times'];
//P['divide'] = P['div'];
//P['remainder'] = P['mod'];
//P['compareTo'] = P['cmp'];
//P['negate'] = P['neg'];


// EXPORT
module.exports = BigNumber;
